Diffusion-Weighted Imaging (DWI) Flashcards
What do we want to measure?
Brain microstructure
• The microstructure is detector of the brain at the micron scale – the scale of the individual scales
• The details of the microstructure – the sides of the cellular domain/cell body – how many dendrite and neurite there are in general in a specific FMRI voxel
• From that density we can infer how healthy is the tissue and what is going on if there is a pathology
What is the principle of MRI?
- It uses the endogenous molecules in your tissue
- Establish equilibrium on these molecules that are in your body
- The magnetic field of MRI scanner will place all the water molecules in your brain in some equilibrium state and perturb the equilibrium state and measure how fast water in your brain comes back to the equilibrium
- Different tissues impact the water state in a different way and provide different contrast in the brain
- We can measure the water density in the brain
- We can measure the relaxation time T1 and T2 or we can measure the diffusion of the water molecules – how water molecules move in your brain tissue
What is diffusion MRI?
- A tool to measure how the water molecules inside your brain or in any biological tissue
- Measures the probability density that your water molecules perform a displacement x after given time t
- Spread of water molecules isotopically in space – the spread is kind of random – it is described by an increase in the displacement to the distance between actual position and initial position with time
- The longer you wait, the more the molecules disperse in the space
What are the basic principles of diffusion MRI (dMRI)?
This method is deeply rooted in the concept that, during their diffusion-driven displacements, molecules probe tissue structure on a microscopic scale, well beyond the usual (millimetric) image resolution
What happens during diffusion times of about 50ms?
Water molecules move in the brain over distance of around 10 micrometre on average, bouncing off, crossing or interacting with many tissue components such as cell membranes, fibres or macromolecules
What does the observation of displacement distribution on a statistical basis provide?
Unique clues to the structural features and the geometric organisation of neural tissues, and to changes in those features with physiological or pathological states
What is diffusion?
A three-dimensional process, and molecular mobility in tissues might not be the same in all directions
What does diffusion anisotropy reflect?
The specific organisation into bundles of myelinated axonal fibres running in parallel
Exploited to map put the orientation in space of the white matter tracks in the brain
What does water diffusion MRI allow ?
Tissue structures to be probed and imaged on a miscoscopic scale, providing unique clues to fine architecture of neural tissues and to changes associated with various physiological and pathological states
What can dMRI be used to map?
The orientation in space of the white matter tracks in the brain, opening a new window on brain connectivity and brain maturation studies
What is the concept of dMRI?
Produce MRI-based quantitative maps of microscopic, natural displacements of water molecules that occur in brain tissues as part of the physical diffusion process
What does molecular diffusion refer to?
Random translational motion of molecules (Brownian motion) that result from thermal energy carried by these molecules - well characterised by Einstein
What happens in a free medium?
During a given time interval, molecular displacements obey a three-dimensional Gaussian distribution - molecules travel randomly in space over a distance that is statistically well described by a diffusion coefficient (D)
What does the diffusion coefficient depend on?
- Size (mass) of the molecules
- Temperature
- Nature (viscosity) of the medium
What is the actual diffusion distance?
Reduced compared with that of free water, and the displacement distribution is no longer Gaussian
At longer diffusion times the effects of the obstacles predominate
What does the non-invasive observation of the water diffusion-driven displacement distribution in vivo provide?
clues to the fine structural features and geometric organization of neural tissues, and also to changes in these features with physiological and pathological states
How can the magnetic resonance signal be made to be sensitive to diffusion through?
The use of a pair of sharp magnetic field gradient pulses (Stejskal,1965), the duration and the separation of which can be adjusted
What happens in homogenous field?
The first pulse magnetically ‘labels’ hydrogen nuclei (or protons) that are carried by water molecules according to their spatial location
The second pulse is introduced slightly later to detect changes in the location of nuclei; the displacement history of nuclei that occurred during the time interval between the two pulses
What are the typical shapes that the dispersed water molecules take in the brain?
In the gray matter we have lots of unrestricted space and the shape is spherical - they disperse freely. In the white matter however they take cylinder like shapes as this is where the axons are and water molecules tend to move along the axons and not across
What is the stimulated-echo sequence?
Allows the effective diffusion time to be increased without penalising the signal by T2 relaxation effect
What is a stimulated echo generated from?
Sequence consisting of three radiofrequency (RF) pulse separated by time intervals T1 and T2. Gradient pulses must be inserted within the first and the third periods of the stimulated echo sequence
What is the principle of a standard spin echo?
- Measure T2 relaxation
- You have 90-degree pulse and 180-degree pulse
- Flip the magnetisation onto the transverse plane
- The phases start randomly dephasing due to in-coherence
- After the 180-degree pulse you flip the magnetisation so all the dephases now have a negative sign
- If you wait in time – you are able to rephase all the spin and get the signal
- You get a signal equal to the maximum
What is the principle of pulsed-gradient spin echo?
- If we applied the gradient pulse, after the 180 pulse in a controlled way – dephase the spins
- Along the direction r so that each spin is in the position 1,2,3 – they acquire a specific phase which depends where they are on the voxel
- We can define q vector – the wave vector associated to the position in this way
- G – gradient strength and the little delta is the duration
- The separation between the two pulses is big delta
- Q vector is the vector in the Fourier space for the position of all the pools of molecules
- Q vector depends on the strength of the gradient and the duration of the gradient
What is required if you want to measure fine movement?
You need a high q - all strong gradient
How do you obtain diffusion-weighted images?
- Orientate in the direction of the fibres of the white matter axons in the corpus callosum
- In this direction, since it is parallel to the directions of the axons, they move very fast
- Because they move very fast that r2-r1 is big and the signal drops but if I change q and point it orthogonal – measure how fast they are moving orthogonal – they do not move much and r2-r1 is smaller and the signal is higher
- Probing different displacements
What is spin displacement density?
• The signal we measure is proportional to the displacement of r2-r1 and q vector [sequence parameter you set in the machine]
• There is a relationship between the signal we measure and the probability of the displacement of the molecules
• The signal is the Fourier Transform
- I can access the parameters by inverse Fourier Transform
• The signal is the Fourier Transform of the displacement probability density function of water molecule
• Normalised by a constant which is dependent by proton density
What does changes in the water ADC during neuronal activation reflect?
Transient microstructural changes of the neurons or the glial cells during activation
What is ADC?
measure of the magnitude of diffusion (of water molecules) within tissue, and is commonly clinically calculated using MRI with diffusion-weighted imaging (DWI)
Is the measured or observed diffusion coefficient obtained from an experiment
What does ADC depend on?
Reflects not only true diffusion, but depends on spatial orientation, microscopic perfusion, bulk tissue motion and pulse sequence timing
What can be characterised by single diffusion coefficient D?
- Fluids
- Gels
- Homogenous materials
Representing the flux of water or small particles via Brownian motion across a surface during a period of time
What does ADC refer to?
Mean diffusion in a voxel, sometimes taken as the sum or average value of the tensor’s diagonal elements
What is the b-value?
A factor that reflects the strength and timing of gradients used to generate diffusion-weighted images
The higher the b-value, the stronger the diffusion effects
What isS = Soe−bD?
he term e−bD thus behaves very much like the T2-weighting term e−TE/T2 found in many other pulse sequences. The value of b is selected by the operator prior to imaging. This choice controls the degree of observed diffusion-weighting similar to the way choosing TE affects T2-weighting
What do most modern DWI pulse sequence consist of?
two strong gradient pulses of magnitude (G) and duration (δ), separated by time interval (Δ).
What does b-value depend on?
strength, duration, and spacing of these pulsed gradients. A larger b-value is achieved with increasing the gradient amplitude and duration and by widening the interval between gradient pulses.
What does the optimal choice of b-value depend upon?
field strength, number of signals averaged, anatomical features, and predicted pathology.
What is a problem as b-values are increased?
Mechanical vibration artefacts
What do most routine clinical DWI currently use?
b-values between 0 and 1000, with slightly lower values being used outside the central nervous system.
What does the value of each tensor element depend on?
Frame of reference in which it is measured
How can individual tensor element be measured?
Typically begin in the so-called laboratory (x-y-z) frame which for clinical mRI is typically aligned with the patients body and main magnetic field Gradients are applied in different directions and several sets of raw data (source) images are obtained.
How are estimate for each tensor component made?
After some filtering and other mathematical corrections, linear regression techniques are applied to the data
What is the diffusion tensor matrix?
Symmetric with only 6 unique element
To estimate all of them we need a minimum of 7 measurement: one baseline (b0) and 6 source data sets
What are the values we calculate for each tensor component ?
not unique, being dependent on the (x-y-z) frame of reference chosen for measurement. Had we selected a different coordinate system (x’-y’-z’) not aligned with the patient but at some arbitrary angle, the calculated values (Dx’x’ or Dx’y’) would have been completely different.
What is the optimal coordinate system for diffusion tensor based upon?
Diffusion ellipsoid whose main axis is parallel to the principal diffusion direction within a voxel. This principal axis often corresponds to anatomic features such as white matter tracts or fascial plans
What are the major and minor axes of diffusion ellisoid defined by?
thee orthogonal unit vectors (ε1, ε2, and ε3) known as eigenvectors. The length of each eigenvector (εi) is multiplied by a factor λi, called the eigenvalue. The eigenvalues of the ellipsoid are proportional to Einstein’s root mean squared diffusion displacement in each direction. By convention, eigenvalues are labeled in descending order of magnitude (λ1 ≥ λ2 ≥ λ3)
What is an additional benefit of using diffusion ellipsoid?
this frame of reference, the off-diagonal elements disappear. The set of eigenvalues define a matrix with only 3 diagonal elements denoted by the symbol Λ (“capital lambda”) that appears in many advanced treatises about diffusion tensors
What are lamda 1 ~ lamda 2 ~ lamda 3 -Isotropic?
Grey matter, CSF
1 2» 3 – Oblate
White matter
1» 2 3 – Prolate
white matter
What is fractional anisotropy
is an index for the amount of diffusion asymmetry within a voxel, defined in terms of its eigenvaluesThe value of FA varies between 0 and 1. For perfect isotropic diffusion, λ1 = λ2 = λ3, the diffusion ellipsoid is a sphere, and FA = 0. With progressive diffusion anisotropy, the eigenvalues become more unequal, the ellipsoid becomes more elongated, and the FA → 1.
What is FA map?
gray-scale display of FA values across the image. Brighter areas are more anisotropic than darker areas
Principal Diffusion Direction Map
This is a map that assigns colors to voxels based on a combination of anisotropy and direction. It is also called the colored fractional anisotropy map, fiber direction map or diffusion texture map. The color assignment is arbitrary, but the typical convention is to have the orientation of the principal eigenvector (ε1) control hue and fractional anisotropy (FA) control brightness. Specifically, if ε1 makes angles α, β, and γ with respect to the to the laboratory x-, y-, and z-axes, the color scheme might be apportioned in the ratios:
Red = FA • cos α
Green = FA • cos β
Blue = FA • cos γ
Grey-matter
Lots of unrestricted space and the shape is spherical - they disperse freely
White matter
Cyclinder like shape - where the axonr are and water molecules tend to move along the axons and not across
What is one of the most satisfactory methods for measuring self-diffusion coefficients ?
Spin-echo method
What is used to measure T1 and T2 relaxation?
Radio frequency sequence coupled with a sequence of gradient pulses
Use magnetic field gradients controlled perturbations of magnetic field to encode the phase of each spins
What is spin echo a standard sequence to measure?
T2 relaxation
Have 90 degree pulse and 180 degree pulse
90 degree pulse - flip all the magnetisation into the transverse plane
- the phases start to randomly de phase due to incoherence
After 180- flip the magnetisation so that all the dephased phases are negative signs
- wait an equivalent time - able to rephase all the spins and get the signal
Echo - get a signal that is equal to the maximum
Apply the gradient pulse - after 180 in a controlled way, dephase my spins (along the direction r) - acquire a specific phase
How is the q vector defined ?
The wave vector associated to the position
G- gradient strength
Little delta - duration
What is the big delta?
The separation between the two pulses
Why do spins move?
There is diffusion
Change position after time
Signal loss
The more the water molecules move - the more the signal decays because the difference between the final phase and initial phase is larger
What happens if the spins do not move?
Get the maximum signal
What happens if the signal moves a little bit?
The signal decays
What happens if the spins moves even further?
The signal decays further because there is more dephasing
What is q?
Duration x the gradient strength is a vector -you can orientate it in space
What happens if Q is changed and is pointing orthogonal?
Measuring how fast the water molecules are diffusing orthogonal to the boundary of the myelin - doesn’t move much - R2-R1 is smaller and the signal is higher
What is there a relationship between?
The signal that is measured and the probability of the displacement of molecules
Fourier transform
What is the signal?
Fourier transform of the displacement probability density function of the water molecules
Normalised by some constant which is dependent on proton density
What is the probability density function of water displacement?
A Gaussian - they can explore all of the space
The variance of the Gaussian depends on the time and a constant d (diffusion coefficient)
What does the diffusion coefficient give?
A measure of how fast my water molecules spread into the space
For Gaussian distribution, what is there a linear relarionship between?
Time and the b value
What is the Fourier transform of a Gaussian?
An exponential
What is a unique parameter b?
Diffusion time vector
What happens in the case of free diffusion?
When you have a Gaussian probability density function for water molecules displacement
The signal is proportional to e-bd
What gives the b value?
G, theta and delta
What is assumed for signalling diffusion ?
equal to e(-bd)
D- apparent diffusion coefficient (ADC) - apparent because it depends on the parameter that you set on your machine
ADC map
Diffusivities are higher in the CSF - water molecules are free to move - move faster
Lower in the tissue where they are constrained by the cellular membrane in different ways
Where does the signal drop faster?
Where the water molecules travels faster
Free water - black - lose all the signal
Tissue - signal - denser and has a lot of stuff hindering the diffusion
What does the rate depend on?
How the tissue composed
What happens if the diffusion is not isotropic?
Molecules can move faster in one direction and slower in another
What is a tensor?
A matrix 3 by 3
Giving you value in different direction space
What does D value indicate?
How fast they go in the x,y and z direction - all the combinations of different directions
What does the diffusion tensor determine?
The ellipsoidal shape and orientations of the contours
What is e1?
The main direction corresponding tor the faster diffusion
What is e2 + e3?
Orthogonal direction corresponding to the slowest diffusion
What can the diffusion tensor be described by?
An ellipsoid
The long axis of the ellipsoid reflects the principal diffusion direction
What does the main eigenvector give?
The direction of the fibre
How tractography works
What are examples of shape for the diffusion tensor in equal brain region?
Grey matter, CSF - isotropic
- expect the 3 eigen vectors to have similar values
- CSF: all equal but high
- Grey matter: all equal but low
White matter can be oblate or prolate
Oblate - when different directions are converging
Prolate - one fibre bundle going in one specific direction
What does diffusion tensor have?
6 independent elements - atleast 6 independent measurement
What is normalisation constant?
Proportional to proton density
Extra parameter we need to estimate
